Mid-gap states and Kondo effect in disordered graphene

Recent experiments on graphene flakes with short range scattering defects have stengthen the interest on Kondo physics in graphene systems. The experimental data show a temperature dependence of the resistivity consistent with the low-temperature Kondo screening of local magnetic moments. While the linear dispersion in the density of states in graphene justify a pseudogap Kondo model showing a rich variety of quantum critical behavior as a function of the gate-controlled chemical potential, the presence of disorder can alter this effect in favor of the ``standard'' Kondo model, with a Fermi-liquid ground state. We study these effects with different numerical methods. Tight-binding calculations for diluted scattering defects show the appearance of quasi-localized midgap states in the local density of states at the vicinity of the charge neutrality point. This leads to the formulation a Anderson-like model of localized states within the graphene matrix, which may lead to a Kondo screening consistent with the experiments. To verify this hypothesis, we perform numerical renormalization group (NRG) calculations to study the gate-dependence of the Kondo temperature and the transport properties of this model.